The accuracy of cell vertex finite volume methods on quadrilateral meshes. (English) Zbl 0767.65072

Süli, Endre

Math. Comput. 59, No. 200, 359-382 (1992).

Author’s summary: For linear first-order hyperbolic equations in two dimensions we restate the cell vertex finite volume scheme as a finite element method. On structured meshes consisting of distorted quadrilaterals, the global error is shown to be of second order in various mesh-dependent norms, provided that the quadrilaterals are close to parallelograms in the sense that the distance between the midpoints of the diagonals is of the same order as the measure of the quadrilateral.
On tensor product nonuniform meshes, the cell vertex scheme coincides with the familiar box scheme. In this case, second-order accuracy is shown without any additional assumption on the regularity of the mesh, which explains the insensitivity of the cell vertex scheme to mesh stretching in the coordinate directions, observed in practice.

Reviewer: J.Albrycht (Poznań)

MSC:

65M15	Error bounds for initial value and initial-boundary value problems involving PDEs
65M60	Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
65M12	Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
76H05	Transonic flows
35L45	Initial value problems for first-order hyperbolic systems

Keywords:

error bounds; stability; linear first-order hyperbolic equations; cell vertex finite volume scheme; finite element method; tensor product nonuniform meshes; box scheme; second-order accuracy